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Probability
1.Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Answer:Option 1

Explanation:

Solution:
Here, S = {1, 2, 3, 4, ...., 19, 20}.
Let E = event of getting a multiple of 3 or 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 20}.
P(E)=n(E)n(S)=920

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2.A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

Answer:Option 1

Explanation:

Solution:
Totalnumberofballs=(2+3+2)=7.LetSbethesamplespace.Then,n(S)=Numberofwaysofdrawing2ballsoutof7=7C2=(7×6)(2×1)=21.LetE = Eventofdrawing2balls,noneofwhichisblue.n(E)=Numberofwaysofdrawing2ballsoutof(2 + 3)balls=5C2=(5×4)(2×1)=10.P(E)=n(E)n(S)=1021.

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3.In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

Answer:Option 1

Explanation:

Solution:
Totalnumberofballs=(8+7+6)=21.LetE = eventthattheballdrawnis neitherrednorgreen = eventthattheballdrawnisblue.n(E)=7.P(E)=n(E)n(S)=721=13

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4.Three unbiased coins are tossed. What is the probability of getting at most two heads?

Answer:Option 1

Explanation:

Solution:
Getting at most Two heads means 0 to 2 but not more than 2.
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E)=n(E)n(S)=78

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5.Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is even?

Answer:Option 1

Explanation:

Solution:
In a simultaneous throw of two dice, we have n(S) = (6 x 6) = 36.

Then, E= {(1, 2), (1, 4), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 2), (3, 4), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 2), (5, 4), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
n(E)=27P(E)=n(E)n(S)=2736=34

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6.In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:

Answer:Option 1

Explanation:

Solution:
Let S be the sample space and E be the event of selecting 1 girl and 2 boys.
Then, n(S) = Number ways of selecting 3 students out of 25.
=25C3=(25×24×23)(3×2×1)=2300.n(E)=(10C1×15C2)=[10×(15×14)(2×1)]=1050.P(E)=n(E)n(S)=10502300=2146.

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7.In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Answer:Option 1

Explanation:

Solution:
P(gettingaprize)=1010+25=1035=27

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8.Two dice are tossed. The probability that the total score is a prime number is:

Answer:Option 1

Explanation:

Solution:
Clearly, n(S) = (6 x 6) = 36.
Let E = Event that the sum is a prime number.Then
E = { (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5) }
n(E)=15.P(E)=n(E)n(S)=1536=512

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9.A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart is:

Answer:Option 1

Explanation:

Solution:
Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E)=n(E)n(S)=252=126

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10.A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is:

Answer:Option 1

Explanation:

Solution:
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15
=15C3=(15×14×13)(3×2×1)=455.LetE = eventofgettingallthe3redballsn(E)=5C3=5C2=(5×4)(2×1)=10.P(E)=n(E)n(S)=10455=291.

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